In [1]} a new class of local models was introduced. The underlying principle behind them mirrors observations from the empirical studies of flocks [2]}, [3]}, [4]} which postulate that the probe horizon of given agent \(x\)  is determined, less by the Euclidean distance, and more by the density of the crowd around \(x\) . Thus, in thicker crowds communication spreads slower than in thinner ones. Communication based on the density is called topological, as opposed to metric which is based on the Euclidean distance. To measure topological distance we implement a metric determined by the mass of a communication domain \(\Omega (x,y)\)  between \(x\)  and \(y\) :
\(d(x,y) = \left(\int _{\Omega (x,y)} \rho (\xi ,t) \, \mbox{d}\xi \right)^{1/n}.\) 
